Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

作     者：Ghulam MUSTAFA 

作者机构：Department of MathematicsThe Islamia University of BahawalpurBahawalpur 63100Pakistan 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2017年第38卷第5期

页      面：1077-1092页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Research Program for Universities(No.3183) 

主　　题：几何方法 模型选择 细分 统计 广义算法 均匀B样条 曲线族 混合函数 

摘      要：The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.